1. Field of the Invention
This invention relates to a method of image restoration. More particularly, it relates to a method of image restoration which is used to improve the quality of image pictures obtained from a scanning electron microscopy (SEM).
2. Description of the Prior Art
The following techniques have been used widely as image restoration process to improve the quality of image pictures.
(1) Smoothing process
This process shows its real ability when the difference of frequency spectrum between the signal component and the noise component of an input signal is relatively large. Three operating methods for this process are as follows.
1) Convolution process: this is a method to convolute obtained image pictures directly. A spatial filtering process and a median filtering process are included in this method.
2) Frequency region process: this is a method to execute Fourier transform onto obtained image data, first, in order to convert them into the data expressed in a frequency region, then, to apply a filter (such as a Gauss filter, a Haming filter, a Haning window filter etc.) to the data, and finally to execute inverte Fourier transform.
(2) Averaging process
This process accumulates data for every picture element by repeating inputs, and calculates the average among the data for each of the picture elements. Unlike the smoothing process, this method does not require a large difference in frequency spectrum between the signal component and the noise component of the image picture.
Among the smoothing processes mentioned above, the convolution process process is widely used as a low pass filter especially in a relatively low frequency region. The aim of this process is, thus, to detect embedded signals, which have relatively low frequencies, from among random noise having relatively high frequency component. In a prior art, therefore, said smoothing process is used in combination with said averaging process for the image restoration. In other words, in order to reconstruct an image picture, the noise component, which has different frequency spectrum from the signal component, is removed by the smoothing process, while the other random noise are removed by the averaging process in order to reconstruct an image picture.
In the process mentioned above, let the variance of noise in an original image picture, which has not been processed yet, be .sigma..sub.org.sup.2, the variance of noise in an image picture, which has been subjected to the averaging process, be .sigma..sub.avr.sup.2, the variance of noise in an image picture, which has been subjected to the smoothing process, be .sigma..sub.smo.sup.2, and the addition time or the sample points of smoothing be N. In the case where the noise have no correlation to each other, the relation between .sigma..sub.smo.sup.2 and .sigma..sub.avr.sup.2 can be expressed as follows. EQU {.sigma..sub.smo.sup.2 .vertline..sigma..sub.avr.sup.2 }=.sigma..sub.org.sup.2 /N (1)
On the other hand, if the noise have a perfect correlation to signal, said relation can be expressed as follows. EQU {.sigma..sub.smo.sup.2 .vertline..sigma..sub.avr.sup.2 }=.sigma..sub.org.sup.2 ( 2)
Usually, each noise has some degree of correlation for signal so that the effect has an intermediate value between said (1) and (2). As understood from equation (1), the effect of noise reduction is improved as the value N increases. On the other hand, distortion of the signal increases gradually as the value N increases. This is because there is an opposite relation between the noise reduction and the distortion of signals.
In order to reconstruct fine changes on an image picture, therefore, it is necessary to reduce the smoothing points and to increase the number of additions as much as possible. To accomplish this situation, objects should be ones in which the precision of synchronization at additions is high enough and no change during these additions occurs according to time change.
In the image restoration process of the prior art mentioned above, the following disadvantages occur according to the radiation of electron beams.
(1) A phenomenon occurs, in which the diameter of grains become large or a film is formed on a grain surface, as the sample observation by an SEM continues. This phenomenon is called "contamination", and is caused by carbide, which exists in a specimen chamber and change its quality so as to adhere to the sample surface by electron bombardment. The established theory of this mechanism is the surface diffusion theory. In other words, this phenomenon is caused by hydrocarbon molecules which change in quality to reduce the surface area and adhere to the sample surface by electron bombardment. The molecules are, then, supplied to electron bombardment areas by surface diffusion. As a result of this contamination phenomenon, the brightness of SEM image pictures decreases as the time progress. Therefore, in said averaging process, the addition times by which fine changes in objects are found, cannot be made so large. From said model, the contamination rate K is calculated as follows. EQU K.varies.J.sub.o /r.sub.o.sup.2 (1+J.sub.o .sigma..tau./e)
In the equation described above, J.sub.o means the current gray level of the electron beam, r.sub.o means the radius of the electron beam, .sigma. means the sectional area of contamination, and .tau. means the residence time of diffused molecules.
(2) During the observation of insulators by an SEM, white shining parts arise on the image picture when the acceleration voltage of the electron beam goes too high beyond a certain voltage. In this case, a distortion sometimes arises on the image picture. The cause of this phenomenon is considered to be as follows. When the acceleration voltage of the electron beam becomes too high, as mentioned above, the ratio of secondary electron release from a sample becomes less than one. As a result, the sample surface is negatively charged to cause said phenomenon. This phenomenon is called the charge-up phenomenon. The waveforms of signals become distorted as a result of this charge-up phenomenon. In the measurement of the line width of signals, therefore, the degree of dispersion among measured values increases to cause wrong interpretation for observed image pictures.
According to said two points, especially in the observation of insulators by an SEM, an electron beam having high energy cannot be used to improve the resolution of image pictures. Therefore, an electron beam having relatively low energy, compared to the case in which metal samples are observed, should be used to observe insulator samples. It is also necessary to reduce addition times in the image restorating process, in order to prevent the generation of contamination. As a result, fine changes existing in an object cannot be found clearly from insulator samples by the prior art image restoration processes mentioned above. A novel process for image restoration is, therefore, necessary for the observation of insulator samples by an SEM.
The details concerning the above mentioned problems regarding electron bombardment by an SEM are described in "Scanning Electron Microscopy", by L. Reimer, Springer Verlag, N.Y., 1985.